Question: The grades on a chemistry midterm at Oak are normally distributed with $\mu = 69$ and $\sigma = 5.5$. Emily earned a $57$ on the exam. Find the z-score for Emily's exam grade. Round to two decimal places.
Answer: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Emily's exam grade by subtracting the mean $(\mu)$ from her grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{57 - {69}}{{5.5}}} $ ${ z \approx -2.18}$ The z-score is $-2.18$. In other words, Emily's score was $2.18$ standard deviations below the mean.